I'm currently studying Ethereum's PoS and a sentence on the relationship between fault tolerance and network delays caught my attention in the Proof of Stake FAQ. Quoting Vitalik:
In this model, the protocol has 50% fault tolerance assuming zero network latency, ~46% (Ethereum) and ~49.5% (Bitcoin) fault tolerance under actually observed conditions, but goes down to 33% if network latency is equal to the block time, and reduces to zero as network latency approaches infinity.
I understand the fault tolerance threshold should be 50% in any PoW-based consensus because that's the hashpower needed to disrupt (and possibly control) the PoW algorithm. However, Vitalik implies the threshold is inversely proportional to network latency.
Can someone explain why this happens and how exactly does the fault tolerance threshold depend on network latency?